Construct rhombus

Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm

Correct answer:

a =  0 cm

Step-by-step explanation:

$$\begin{gathered} 1.AC,\mathrm{\mid }AC\mathrm{\mid }=8cm \\ 2.S;S\in AC,\mathrm{\mid }SA\mathrm{\mid }=\mathrm{\mid }SC\mathrm{\mid } \\ 3.p;p\perp AC,S\in p \\ 4.k;k(S,r=1.5cm) \\ 5.S_1;S_1\in AS,\mathrm{\mid }S{S}_1\mathrm{\mid }=\mathrm{\mid }A{S}_1\mathrm{\mid } \\ 6.S_2;S_2\in SC,\mathrm{\mid }S{S}_1\mathrm{\mid }=\mathrm{\mid }C{S}_1\mathrm{\mid } \\ 7.t_1;t_1(S_1,r=\mathrm{\mid }AS\mathrm{\mid }) \\ 8.t_2;t_2(S_2,r=\mathrm{\mid }CS\mathrm{\mid }) \\ 9.T_1,2;T_1,2=t_1\cap k \\ 9.T_3,4;T_3,4=t_2\cap k \\ 10.A{T}_1;A{T}_2;C{T}_3;C{T}_4 \\ 11.B=A{T}_1\cap C{T}_3 \\ 12.D=A{T}_2\cap C{T}_4 \\ 13.ABCD \\ a=0\text{ cm} \end{gathered}$$

Try another example

Related math problems and questions:

• Construct
  Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.
• Right triangle
  Draw a right triangle ABC if |AB| = 5 cm |BC| = 3 cm, |AC| = 4 cm. Draw Thales circle above the hypotenuse of the triangle ABC.
• Complete construction
  Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
• Circle tangent
  It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
• Rhombus construction
  Construct ABCD rhombus if its diagonal AC=9 cm and side AB = 6 cm. Inscribe a circle in it touching all sides...
• Draw a trapezoid
  Draw a trapezoid if given a = 7 cm, b = 4 cm, c = 3.5 cm, diagonal AC = 5cm. Solve as a construction task.
• Tangents construct
  The circle k is given k (S; 2.5 cm) and an outer line p. Construct a tangent t of the circle that has with a line p angle 60°. How many solutions have the task?
• Two heights and a side
  Construct triangle ABC when the given side is c = 7 cm, height to side a va = 5 cm and height to side b: vb = 4 cm.
• Rhombus
  It is given a rhombus of side length a = 19 cm. Touchpoints of inscribed circle divided his sides into sections a₁ = 5 cm and a₂ = 14 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
• Construct 1
  Construct a triangle ABC, a = 7 cm, b = 9 cm with right angle at C, construct the axis of all three sides. Measure the length of side c (and write).
• Triangle SSA
  Construct a triangle ABC if |AB| = 5cm v_a = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
• Construct
  Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
• Rhombus ABCD
  Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
• Diagonals
  Draw a square ABCD whose diagonals have a length of 6 cm
• Outer contact of circles
  Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contacts. Calculate the perimeter of the triangle S₁S₂S₃.
• Rhombus and inscribed circle
  It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
• Rhombus MATH
  Construct a rhombus M A T H with diagonal MT=4cm, angle MAT=120°